Regarding all pores in rock as a system consisting of spherical pore and capillary pores, this paper presents a model of Sphere‐Capillary. After all pores are divided into different groups by their radii, the relaxation time of each group can be calculated with the Sphere‐Capillary Model. The transversal relaxation time (T2i), spaced on the Sphere‐Capillary Model, can be utilized to conduct the inversion of NMR relaxation signal. Our research suggests that the T2 distributions from the inversion are relative to special pore structures defined by the Sphere‐Capillary model. Using different Sphere‐Capillary Models to derive different relaxation times, then conduct the inversion relaxation signal with the relaxation time. When a T2 distribution fits the relaxation signal in the least squares, the pore structure defined by the Sphere‐Capillary Model characterizes the pore system in rock best. Data from lab NMR measurements are analyzed with the Sphere‐Capillary Model, and the results are compared with the pressure data from mercury injection. This research shows that the Sphere‐Capillary Model describes properly the relaxation characteristic relative to pore structure. Furthermore, the relaxation characteristic may hold a relationship with pore fluids.

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Many cases have indicated that the conductivity and permeability of porous media may decrease to zero at a nonzero percolation porosity instead of zero porosity. However, there is still a lack of a theoretical basis for the percolation mechanisms of the conductivity and permeability. In this paper, the analytical percolation expressions of both conductivity and permeability are derived based on fractal theory by introducing the critical porosity. The percolation models of the conductivity and permeability were found to be closely related to the critical porosity and microstructural parameters. The simulation results demonstrated that the existence of the critical could lead to the non-Archie phenomenon. Meanwhile, the increasing critical porosity could significantly decrease the permeability and the conductivity at low porosity. Besides, the complex microstructure could result in more stagnant pores and a higher critical porosity. This study proves the importance of the critical porosity in accurately evaluating the conductivity and permeability, and reveals the percolation mechanisms of the conductivity and permeability in complex reservoirs. By comparing the predicted conductivity and permeability with the available experimental data, the validity of the proposed percolation models is verified.

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